Question

A boat operator wants to offer tours of San Francisco Bay. His profit P for a trip can be modeled by P(x) = −2x^2 + 120x − 788, where x is the cost per ticket. What range of ticket prices will generate a profit of at least $500?

Answer 1

14 to 46 tickets

Explanation:

Step 1: Set up the equation

500 ≤ -2x² + 120x - 788

Step 2: Solve for x

0 ≤ -2x² + 120x - 1288

0 ≤ -2(x² - 60x + 644)

0 ≤ x² - 60x + 644

0 ≤ (x - 46)(x - 14)

14 ≤ x ≤ 46

Alternatively, we can graph the equation and determine the range by looking for where y = 500